Paint by Numbers
Lesson Idea by:
Cindy Botnen, Hollywood Middle School, Kelowna, B.C.
may think that painting a house is just about picking the right color
-- but it involves way more than that. A house painter needs good
people skills along with technical know-how. Plus, a painter has to use
more math than you might expect!
Joe Wolfe owns his own house-painting business.
use math for pretty much everything," he says. "From wages, to
determining how much paint I'll need, to figuring out paint-water
ratios and pricing a job. Every aspect of painting requires some math."
are contracted by clients to paint all kinds of buildings, both
interiors and exteriors. They paint walls, ceilings, floors and
cabinets using varnish, enamels, paint and other finishes.
need more than a keen eye and a steady hand to be successful. They also
have to be good at business. Often, getting a painting contract
requires a painter to make a bid. A bid is an offer to do work or
supply products at a certain price.
client may ask three or four painters to bid on a job. Then, the client
picks one, usually the cheapest. So, if a painter's bid is too high, a
competitor will get the work. If the bid is too low, the painter won't
make any money. Once a bid is accepted, the price cannot be changed.
Due to these factors, a painter has to be careful in calculating the
amount of work needed and estimating a bid.
into groups of four and together prepare a bid to paint your classroom.
You will need several paint store flyers, measuring tapes and
calculators. Use the Student Worksheet below to guide your work.
a painting company and give it a name. Measure the walls to calculate
how many square feet you will have to paint. Discuss whether you will
paint around the bulletin boards or take them off. Do you need to
subtract the space taken up by windows and doors? Is it necessary to
get that fussy when preparing an estimate? Does the size of the job
have anything to do with how precise your estimate should be?
many gallons of paint will you need? (Note that one gallon of paint
will cover 400 to 500 square feet of wall space.) What supplies will
you need, and how much will they cost? Determine how many painters will
be painting, for how many hours, and at what wage.
is your estimate? Is it reasonable? That is, will the estimate be low
enough so you'll get the job, but high enough to give you some profit?
Prepare the estimate and submit it to your teacher.
As a class, discuss the following:
- How important is it to prepare a precise estimate?
- Does the size of the job have anything to do with how precise an estimate should be?
- What happens if the estimate is too low? Too high?
- Why is area an important mathematical concept for house painters?
- Who else might need to understand area and use it in their work?
Review what you know about area.
The formula for area is:
area = length x width
calculation tells you the total area to be painted. Now you've got to
calculate the amount of materials -- be it paint or wallpaper -- needed
to cover that area. To calculate the amount of materials needed, divide
the total area to be covered by the area the material will cover.
the packaging on the material will say how much area the product will
cover. For example, a gallon of paint will cover 400 to 500 square
feet, while a single roll of wallpaper will cover about 25 square feet.
and wallpaper are two of the more common wall coverings. Yet there are
plenty of others. You may also need to calculate area for wallpaper
borders, wainscoting, wooden paneling, and even fabric for cloth wall
coverings. Clients may also want walls covered with big murals or
collages made up of tiny little pictures.
to the Practice section for a moment. Your teacher is a little strange
and wants one wall covered with $100 bills. * Estimate how many $100
bills you think you would need before you do any calculations.
Now, use math to make a more precise estimate. A $100 bill measures 2.75 x 6 inches. How many would you need to cover the wall?
your guess match the estimate? Are you even close? Considering that the
cost of supplies in this case is $100 per bill, how important are good
a bid to renovate your own room or another room in your home. Consider
painting the walls, changing the flooring and picking new window
Get samples and
prices from suppliers such as interior decorators or hardware shops.
Often, suppliers are happy to give you discontinued sample books of
fabrics, flooring and wallpaper. Pick your colors and fabrics to make a
"color board" displaying your choices. Be sure to show your
measurements and estimate of the costs involved.
just been called to give an estimate for a paint job. It's a big house
and the owner wants all of it painted. You must provide a written bid
for the job. You know that the owner is getting bids from other
painters in town. You want to get this job, so you have to prepare a
really good bid.
has five rooms and a hallway. The kitchen is 25 feet by 20 feet. There
are three bedrooms. Bedroom A is 30 feet by 27 feet. Bedroom B is 15
feet by 15 feet, and bedroom C is 12 feet by 10 feet. The living area
is a colossal 30 feet by 35 feet. The hall is 20 feet by four feet.
this case, you estimate that one gallon of paint will cover only 100
square feet because of the kind of paint it is and because of the high
ceilings. Paint costs $18 per gallon plus seven percent tax.
it is such a big job, you may need help. An assistant will cost $7 per
hour and you estimate that you'll need two assistants for about 80
hours each. You figure that you'll be working on the house for 100
hours -- and generally you make $10 per hour. Your usual price is $1.25
per square foot. You estimate that supplies will cost $200.
up your first estimate using $1.25 per square foot. How much money will
you make? Will it cover everything? Can you afford to reduce your price
per square foot? What is your break-even price per square foot?
*Thanks to Dave Sufrin, of Parksville, British Columbia, for his suggestion about using $100 bills in this exercise.
Problem solving; Number Operations 1
Analyze problems and identify the significant factors, demonstrate group skills, and solve real-life problems with formulae
- Measuring tape
- Flyers from paint stores
Student Worksheet: Estimates for Practice Section
Name of paint company:
Items to be considered:
Area of walls to be painted:
Number of gallons of paint required:
Cost of paint:
Estimated cost of painting supplies
(rollers, brushes, pans, drop cloth, clean-up):
Number of painters on the job:
Number of hours to complete job:
Total wages for painters:
Profit that goes into the company
(include possible overruns):
Wages + paint + supplies + profit:
FINAL BID FOR THE JOB:
Solution to Learn
First of all you need to calculate the total area. Remember, the formula is:
area = length x width.
(Please note: This symbol, ^, called a caret, is used to indicate
"to the power of.")
25 ft. by 20 ft.
Total area is 25 ft. x 20 ft.
Area = 500 ft.^2
30 ft. by 27 ft.
Total area is 30 ft. x 27 ft.
Area = 810 ft. ^2
15 ft. by 15 ft.
Total area is 15 ft. x 15 ft.
Area = 225 ft. ^2
10 ft. by 12 ft.
Total area is 10 ft. x 12 ft.
Area = 120 ft.^2
30 ft. by 35 ft.
Total area is 30 ft. x 35 ft.
Area = 1,050 ft.^2
20 ft. by 4 ft.
Total area is 20 ft. x 4 ft.
Area = 80 ft. ^2
Total area of house = area of kitchen + bedroom A + bedroom B + bedroom C + living room + hallway
Total Area = 500+810+225+120+1050+80 ft. ^2
Total Area = 2,785 ft. ^2
First estimate at $1.25 per square foot
= 2,785 ft.^2 x 1.25 ft.^2
= $ 3,481.25
1 gallon will cover 100 ft.^2
x gallons will cover 2,785 ft.^2
2,785 = 100 x
It will take 27.85 gallons of paint to paint the house.
x = 27.85
Round up to the nearest full gallon to get 28.
Paint costs $18 per gallon plus 7 percent tax
Cost = (28 x $18) x 1.07
Cost = ($504) x 1.07
Cost = $539.28
Two assistants @ $7 per hour for 80 hours
Wages = 2 x $7 x 80
Wages = $1,120
B) Your wages = $10 per hour x 100 hours
Wages = $1,000
Total Wages = $560 + $1,000
Total Wages = $2,120
Supplies = $200
Total costs = paint + wages + supplies
Totals Costs = $539.28 + $2,120 + $200
Total Costs = $2,859.28
Your profit on the bid is based on $1.25 per square foot. Estimate based on per square foot price minus costs.
$3,481.25 - $2,859.28 = $621.97
The minimum amount that you could charge per square foot would be:
|Minimum per square foot =
|| Total Cost
|| Area of House
|Minimum per square foot =
|| 2,785 ft. ^2
|Minimum per square foot =
|| ft. ^2
there's an extreme circumstance, I would never bid at cost," says house
painter Joe Wolfe. It's too risky. There's no cushion for overruns in
paint, supplies or labour. The lowest he's ever priced a bid was for
$1.05 per square foot.
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